Module 9 Overview: Investigating Patterns and Recursion

In the year 1202, an Italian mathematician and businessman named Leonardo of Pisa, but more famously known today simply as Fibonacci, asked a theoretical question:

How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on? (Liber-Abaci, pub. 1202)

If you “do the math,” things start a little slowly, but pick up fast, and you have a list of rabbit population numbers that looks like this:

We know this list of numbers as the Fibonacci Sequence. Its pattern is that after the first term, each successive term is the sum of the two preceding terms. This pattern arises when we examine the behavior of many actions and events, well beyond that posed by its author more than 800 years ago. For example, the sunflower’s petal patterns exhibit Fibonacci numbers: the ratio of the number of clockwise spirals to the number of counterclockwise spirals always equals two consecutive numbers in the Fibonacci sequence.

In this module, we will investigate patterns of numbers, and the real-world activities they describe, and learn skills to use these patterns to predict future results.